Question

Water flows through a 2 cm radius hose at a speed of 4 m/s.

What must be the nozzle radius so that the water speed is at 16 m/s?

Answer 1

Let's use the equation of continuity:

$$A_1v_1=A_2v_2,$$ $$\pi r_1^2v_1=\pi r_2^2v_2,$$ $$r_2=\sqrt{\dfrac{r_1^2v_1}{v_2}}=\sqrt{\dfrac{(0.02\ m)^2\times4\ \dfrac{m}{s}}{16\ \dfrac{m}{s}}}=0.01\ m=1\ cm.$$